23
votes
Value of Call Option as Volatility goes to Infinity
The value of a call option does not go to infinity as the volatility goes to infinity. It tends to the discounted value of the forward $F=S_0 e^{(r-q)T}$, which when the dividend yield is zero, ...
- 2,137
20
votes
Accepted
Gamma Pnl vs Vega Pnl
For an option with price $C$, the P$\&$L, with respect to changes of the underlying asset price $S$ and volatility $\sigma$, is given by
\begin{align*}
P\&L = \delta \Delta S + \frac{1}{2}\...
- 20.9k
19
votes
Accepted
Arbitrage Free Volatility Smile
I generally agree with @dm63's answer: A convex (concave) smile around the forward usually indicates and leptokurtic (platykurtic) implied risk-neutral probability density. Both situations can or ...
- 5,939
16
votes
Accepted
Local vol, stochastic vol, implied vol
Along with Gatheral's book, I'd recommend reading Lorenzo Bergomi's "Stochastic Volatility Modelling". The first 2 chapters are available for download on his website. That being said, let me try to ...
- 14.4k
16
votes
Accepted
What is the connection between the risk neutral implied density and the real world density?
I'll outline how you can estimate the (implied) real-world density function from (observed) option prices. Having found this real-world density, you can then compute all sorts of probabilities and ...
- 15.1k
15
votes
Accepted
Is volatility for the next day forecastable? To any extent?
Upon close reading, this appears to be 3 (interesting) questions, not one. I'm not sure if the mods have the tools needed to split it up, so I'm just going to write down the three questions as I see ...
- 739
15
votes
Accepted
SSR definition in Bergomi in relation to sticky strike and sticky delta
Some Notations
It's easy to get lost so let's introduce some notations and let
$$ \sigma : (t, S, K, \tau) \to \sigma(K,\tau; S, t) $$
denote the implied volatility smile prevailing at time $t$ ...
- 14.4k
14
votes
Accepted
Estimate Beta of CAPM from Implied Volatility?
Yes it is a better way.
Just take a look to figure 3, from Buss and Vilkov (2012, RFS):
- 7,807
14
votes
Accepted
Option Price vs. Implied Volatility
I think it's interesting to look at this problem graphically also. I get a different answer, depending on whether the option is ITM, ATM, or OTM. In the plot below, all options have 1-year expiry, ...
- 5,918
14
votes
Accepted
Bergomi: Skew arbitrage
Great question. Let me try to provide some insights and thoughts regarding the points and questions you raised. It may not be a full answer but hopefully it will help connecting the contents in the ...
- 811
13
votes
Accepted
How to exploit calendar arbitrage?
The answer by @HenriK is certainly correct. However, for justification, technique such as the Jensen inequality is needed. For example, since $x^+$ is a convex function, assuming zero interest and ...
- 20.9k
13
votes
Forward implied volatility
From an equities perspective, there are two concepts that should not be confused in my opinion and context should make the distinction self-explicit:
Forward variance swap volatility (A)
Forward ...
- 14.4k
13
votes
Accepted
Options Market Making Used Implied Volatility Surface
Your question is twofold
How a market maker should adjust its quotes on a vol surface with respect to his inventory?
How to adjust the vol surface when a new trade is observed on the markets?
Let me ...
- 11.4k
12
votes
Accepted
Why linear interpolation not appropriate for volatility surface construction?
Note that total implied variance defined as
$$
V(T,K) = T\Sigma(T,K)^2
$$
should be an increasing function of $T$. Otherwise you have a calendar arbitrage (sell the call with shorter expiry and ...
- 3,926
11
votes
Accepted
Why is realized volatility typically lower than implied volatility?
Consider what happens when IV is lower than realised vol. The person long the IV would make money. So there would ideally be no one selling IV if it's lower than realised vol on an average.
Next if ...
- 786
10
votes
Accepted
For pricing, what types of Exotic Options are suitable using Local Volatility Model or a Stochastic Volatility Model?
Whenever you use any model to price anything, all you need to do is make sure you model the underlying dynamics that the product you're pricing actually depends on.
Any product will be dependent on ...
- 2,521
10
votes
What is a regime switch?
Regime switching is another way to describe structural changes in a data series. For example, an inflation timeseries may change states from ARMA to linear as the economy moves from a period of ...
- 949
10
votes
Why is there greater demand for OTM and ITM options than for ATM options?
Either you or some reference you are following is in error here. At-the-money (or at least near-the-money) options are the most liquidly traded. And trading is much more heavy in out-of-the-money ...
- 1,875
10
votes
Implied Volatility of stock on Think or Swim
What they gave you is Newton's formula.
If you have a function $f(x)$ then you can find the value $x_0$ such that
$f(x_0) = 0$ by this method. It uses the derivative $f'$ which in your case is the ...
- 13.6k
10
votes
Accepted
Different versions of sticky strike, moneyness and delta
I feel like your notations are not accurate enough to write what you would like to write.
Let $\Sigma(S;K,T)$ denote the implied volatility of a European vanilla of strike $K$ and maturity $T$ now ...
- 14.4k
10
votes
Accepted
Realized Variance (realized volatility)
The TLDR; to your question:
How can one use realized volatility as a volatility model to do out-of-sample prediction? You extend known models to incorporate additional information procured from high-...
- 4,156
9
votes
Accepted
Delta Hedging with fixed Implied Volatility or floating Implied Volatility?
Generally speaking, in the real world, you'd always want to use the correct implied vol. But you should think of your question in terms of:
(1) Vega mark-to-market (m2m) PnL vs. theta/gamma profile
(...
- 715
9
votes
Calendar Arbitrage in a Vol Surface
In a pure diffusion setting, you can equivalently write no calendar arbitrage constraints:
In terms of implied volatility: total implied variance should be non decreasing in time, and that, for any ...
- 14.4k
9
votes
Accepted
What is implied volatility?
In practice, an implied volatility always refers to the volatility that you need to plug into the Black-Scholes', or Black's, pricing formula to obtain the market price. You may have a different model ...
- 20.9k
9
votes
Accepted
What is a regime switch?
The idea of regime switching in volatility is rooted in the observation that volatility is usually fairly consistent and "mild", and occasionally very high, say during a market crash. The concept goes ...
- 288
9
votes
Why is realized volatility typically lower than implied volatility?
Another theory is that stock indexes do not follow a the lognormal distribution assumption of Black-Scholes. For example U.S. equities measured by the Russell 3000 or S&P 500 have a negative skew ...
9
votes
Accepted
Different volatility surface ( Local vol, Stochastic vol etc.)
I'll answer both of your questions in one go:
Your ideas are correct. If the Black-Scholes model was true, the implied volatility surface would be flat but it is not in real life. Thus, the geometric ...
- 15.1k
9
votes
Accepted
Forward skew generated by Local Vol model
We can demonstrate this via a pricing experiment using QuantLib-Python.
I've defined several utility functions in the code block at the bottom of the answer that you will need to replicate the work.
...
- 2,916
8
votes
What does the VIX formula measure and how does it work?
The other answers have given a good qualitative description of what the VIX measures. In this answer, I will try to give a comprehensive quantitative overview of how the VIX formula works.
What is the ...
Only top scored, non community-wiki answers of a minimum length are eligible